Turn the Instant Pot on the saute function. Add the olive oil, chicken cubes, 1 teaspoon of Italian Seasoning, salt, and pepper to taste.
Cook for the chicken for 3-4 minutes until browned and no longer pink. Remove the chicken and set aside.
Drizzle an additional teaspoon of olive oil in the pot. Add the onions, carrots, and celery. Cook for 3-4 minutes until the veggies are soft and the onions are fragrant.
Add in the garlic and stir.
Add the chicken broth and Italian Seasoning to pot and deglaze the bottom of the pot by scooping up the brown bits in the bottom of the pot.
Add the chicken back to the pot. Top with the broken lasagna noodles. Press down to make sure the noodles are covered in liquid. Add additional broth if needed.
Place the lid on the pot and cook for 5 minutes on Manual > Pressure Cooking.
When the pot indicates it has finished cooking, quick release the steam. Turn the Instant Pot on the saute function.
Open the pot and add the milk, heavy cream, shredded cheese, cream cheese, dry white wine, and spinach. Stir until the cheese has melted.
Combine the flour and water in a separate bowl. Stir and add it to the pot. Stir the soup to thicken.
Cool before serving.